Welcome to the homepage for Probability (Math 4600/6600)! I will post all the homework assignments for the course on this page. Our text for the course is Ward and Gundlach, Introduction to Probability. During Spring 2019, the class meets twice a week at 11:00am-12:10pm TR in Boyd 323. Office hours are Tuesday 3-5:30pm in Boyd 448.
Probability is a deep and fascinating mathematical subject, with its own theory as well as connections to analysis, geometry, and combinatorics. In addition, it’s one of the most useful areas of applied mathematics, as entire careers and disciplines (e.g. actuarial science, quantitative finance, machine learning) rest on a firm understanding of the theory of probability. In addition, there are deep connections between probability and physics, explored in the field of statistical physics.
This is a first course in probability, which will introduce you to the basics of the subject: random variables, distribution functions, expectations, variance, conditional probability and joint distributions, independence, Bayes’ Theorem, the law of large numbers, and the central limit theorem. After this course, you’ll know most of what you need to know to pass the SOA/CAS P/1 exam (and the rest is found in chapters of the book we won’t have time to cover).
Mathematica will be an integral part of the course. The mathematics department has a site license for Mathematica and you can get a copy for your laptop or home computer free of charge. I encourage you to work through some introductory material on Mathematica. Some of the homework assignments and projects will require you to write Mathematica programs, and it’s really helpful to be able to use a computer to check your work.
Syllabus and Policies
Please examine the course syllabus. If you think you can get by with this copy, save a tree! Don’t print it out. The course syllabus lists the various policies for the course (don’t miss the attendance policy). The course is organized by day, with the updated plan for the course visible on our shared Google Calendar. Every day, we’ll have a reading assignment before class (the book is actually very readable) and we’ll open class with a short quiz on the reading. Then we’ll have a discussion of the material in the book, followed by some in-class questions. Homework will be due on Thursdays.
Here are links to my class notes and in-class problems for the course. The classes with computer demonstrations have Mathematica notebooks posted here.
- Lecture 1. Definitions. Outcomes, events, sample spaces. DeMorgan.
- Ward/Gundlach Chapter 2. (Note: I’m going to take this down eventually).
- Lecture 2. Axioms, Inclusion-exclusion principle.
- Ward/Gundlach Chapter 3. (Note: I’m going to take this down eventually.)
- Lecture 3. Independent Events.
- Lecture 4. Good before bad.
- Lecture 5. Conditional probability.
- Lecture 6. Bayes’ Theorem (First Part).
- Lecture 7. Bayes’ Theorem (Second Part).
- Lecture 8. The Gambler’s Ruin (and Electrical Networks).
- Lecture 9. Joint pdfs, independence, and conditioning.
- Markov Chains (notes) See also Chapter 11 of Grimstead and Snell.
Starred problems are assigned for students in MATH 6600. They are extra credit problems for students in MATH 4600. (Note: Please write on your paper next to these problems which class you’re in so that we’ll be sure to grade them correctly.)
- Chapter 1. 3, 7, 9, 12*. Chapter 2. 1, 3, 4, 15, 21, 29*. Due: 1/24/2019.
- Chapter 3. 2, 8, 10. Chapter 4. 4, 6, 8. Chapter 5. 6, 10, 16. Chapter 7. 4, 16, 18*. Extra problem: Bayesian Update. (CoinFlipData.csv). Due: 2/19/19. (Tuesday)
- Chapter 8. 2, 8, 10, 18*. Chapter 9. 2, 6, 10. Due: 2/28/19 (Thursday).
- Chapter 10. 2, 6, 8, 14, 18. Extra problems: More Bayes Theorem Problems. (BiasedCoinData.csv). Due 3/7/19 (Thursday).
- Chapter 11. 2, 8, 12, 16. 20*, 22*. Chapter 12. 4, 8, 18, 22, 26*, 30*. Due 3/21/19 (Thursday after break)
- Markov chain problems. Due Thursday 4/18/19.